Radical Alternatives: How SHOULD Size and Speed/Range Affect Chance to Hit?

[Humabout]

Vicky, you make the assumption that shots fired approximate a uniform distribution, which is not the case. They will be clustered more densely around the actual target and become less dense as you look further out. So the size of the target won't have a quadraric effect on hit chance.

Let's assume a normal distribution of distance from bullseye with a standard deviation of 1 unit. If the target is 1 unit radius, the shooter has about a 68% chance of hitting. If we double the target's radius, he now has a 95% chance of hit. Adding another 1 unit to radius increases his odds of hit to 99.8%. He'll never hit 100%.

Now that addresses target size. Distance effects I'm not sure of. It would definitely increase the standard deviation of the final spread, but at what rate, I don't know. The shooter's own ability to be on target plus the effects of atmospheric conditions would be factors, though.